






"""simple docstring"""


import torch

from diffusers import CMStochasticIterativeScheduler

from .test_schedulers import SchedulerCommonTest




class 						__UpperCamelCase     (     UpperCamelCase						):
					lowercase_    :				List[str]      =  (CMStochasticIterativeScheduler,)
					lowercase_    :				List[Any]      =  10
					def        UpperCAmelCase__ (							self							:	Union[str, Any]     , **UpperCAmelCase							:	Optional[Any]   )	->       Optional[int]:
											lowerCAmelCase   :Any						=			{
											    'num_train_timesteps': 201,
											    'sigma_min': 0.0_0_2,
											    'sigma_max': 8_0.0,
											}

											config.update(**UpperCAmelCase   )
											return config
					def        UpperCAmelCase__ (							self							:	List[str]   )	->       str:
											lowerCAmelCase   :Optional[Any]						=			10

											lowerCAmelCase   :Optional[int]						=			self.get_scheduler_config()
											lowerCAmelCase   :Union[str, Any]						=			self.scheduler_classes[0](**UpperCAmelCase   )

											scheduler.set_timesteps(UpperCAmelCase   )

											lowerCAmelCase   :Optional[Any]						=			scheduler.timesteps[0]
											lowerCAmelCase   :List[Any]						=			scheduler.timesteps[1]

											lowerCAmelCase   :int						=			self.dummy_sample
											lowerCAmelCase   :Union[str, Any]						=			0.1 * sample

											lowerCAmelCase   :List[str]						=			scheduler.step(UpperCAmelCase     , UpperCAmelCase     , UpperCAmelCase   ).prev_sample
											lowerCAmelCase   :List[Any]						=			scheduler.step(UpperCAmelCase     , UpperCAmelCase     , UpperCAmelCase   ).prev_sample

											self.assertEqual(output_a.shape     , sample.shape   )
											self.assertEqual(output_a.shape     , output_a.shape   )
					def        UpperCAmelCase__ (							self							:	List[str]   )	->       Union[str, Any]:
											for timesteps in [10, 50, 100, 1000]:
																	self.check_over_configs(num_train_timesteps=UpperCAmelCase   )
					def        UpperCAmelCase__ (							self							:	Dict   )	->       str:
											for clip_denoised in [True, False]:
																	self.check_over_configs(clip_denoised=UpperCAmelCase   )
					def        UpperCAmelCase__ (							self							:	Union[str, Any]   )	->       List[str]:
											lowerCAmelCase   :Tuple						=			self.scheduler_classes[0]
											lowerCAmelCase   :Dict						=			self.get_scheduler_config()
											lowerCAmelCase   :Optional[int]						=			scheduler_class(**UpperCAmelCase   )

											lowerCAmelCase   :str						=			1
											scheduler.set_timesteps(UpperCAmelCase   )
											lowerCAmelCase   :Optional[Any]						=			scheduler.timesteps

											lowerCAmelCase   :List[str]						=			torch.manual_seed(0   )

											lowerCAmelCase   :Dict						=			self.dummy_model()
											lowerCAmelCase   :Union[str, Any]						=			self.dummy_sample_deter * scheduler.init_noise_sigma

											for i, t in enumerate(UpperCAmelCase   ):
																	# 1. scale model input
																	lowerCAmelCase   :Optional[int]						=			scheduler.scale_model_input(UpperCAmelCase     , UpperCAmelCase   )

																	# 2. predict noise residual
																	lowerCAmelCase   :List[Any]						=			model(UpperCAmelCase     , UpperCAmelCase   )

																	# 3. predict previous sample x_t-1
																	lowerCAmelCase   :str						=			scheduler.step(UpperCAmelCase     , UpperCAmelCase     , UpperCAmelCase     , generator=UpperCAmelCase   ).prev_sample

																	lowerCAmelCase   :Optional[Any]						=			pred_prev_sample

											lowerCAmelCase   :int						=			torch.sum(torch.abs(UpperCAmelCase   )   )
											lowerCAmelCase   :Any						=			torch.mean(torch.abs(UpperCAmelCase   )   )

											assert abs(result_sum.item() - 1_9_2.7_6_1_4   ) < 1e-2
											assert abs(result_mean.item() - 0.2_5_1_0   ) < 1e-3
					def        UpperCAmelCase__ (							self							:	List[str]   )	->       str:
											lowerCAmelCase   :List[str]						=			self.scheduler_classes[0]
											lowerCAmelCase   :int						=			self.get_scheduler_config()
											lowerCAmelCase   :Union[str, Any]						=			scheduler_class(**UpperCAmelCase   )

											lowerCAmelCase   :int						=			[106, 0]
											scheduler.set_timesteps(timesteps=UpperCAmelCase   )
											lowerCAmelCase   :List[str]						=			scheduler.timesteps

											lowerCAmelCase   :List[str]						=			torch.manual_seed(0   )

											lowerCAmelCase   :Dict						=			self.dummy_model()
											lowerCAmelCase   :Any						=			self.dummy_sample_deter * scheduler.init_noise_sigma

											for t in timesteps:
																	# 1. scale model input
																	lowerCAmelCase   :int						=			scheduler.scale_model_input(UpperCAmelCase     , UpperCAmelCase   )

																	# 2. predict noise residual
																	lowerCAmelCase   :int						=			model(UpperCAmelCase     , UpperCAmelCase   )

																	# 3. predict previous sample x_t-1
																	lowerCAmelCase   :str						=			scheduler.step(UpperCAmelCase     , UpperCAmelCase     , UpperCAmelCase     , generator=UpperCAmelCase   ).prev_sample

																	lowerCAmelCase   :Optional[Any]						=			pred_prev_sample

											lowerCAmelCase   :List[Any]						=			torch.sum(torch.abs(UpperCAmelCase   )   )
											lowerCAmelCase   :int						=			torch.mean(torch.abs(UpperCAmelCase   )   )

											assert abs(result_sum.item() - 3_4_7.6_3_5_7   ) < 1e-2
											assert abs(result_mean.item() - 0.4_5_2_7   ) < 1e-3
					def        UpperCAmelCase__ (							self							:	Optional[Any]   )	->       str:
											lowerCAmelCase   :Dict						=			self.scheduler_classes[0]
											lowerCAmelCase   :Optional[int]						=			self.get_scheduler_config()
											lowerCAmelCase   :str						=			scheduler_class(**UpperCAmelCase   )

											lowerCAmelCase   :Any						=			[39, 30, 12, 15, 0]

											with self.assertRaises(UpperCAmelCase     , msg='`timesteps` must be in descending order.'   ):
																	scheduler.set_timesteps(timesteps=UpperCAmelCase   )
					def        UpperCAmelCase__ (							self							:	Union[str, Any]   )	->       Tuple:
											lowerCAmelCase   :Tuple						=			self.scheduler_classes[0]
											lowerCAmelCase   :Union[str, Any]						=			self.get_scheduler_config()
											lowerCAmelCase   :Any						=			scheduler_class(**UpperCAmelCase   )

											lowerCAmelCase   :Tuple						=			[39, 30, 12, 1, 0]
											lowerCAmelCase   :str						=			len(UpperCAmelCase   )

											with self.assertRaises(UpperCAmelCase     , msg='Can only pass one of `num_inference_steps` or `timesteps`.'   ):
																	scheduler.set_timesteps(num_inference_steps=UpperCAmelCase     , timesteps=UpperCAmelCase   )
					def        UpperCAmelCase__ (							self							:	List[str]   )	->       List[Any]:
											lowerCAmelCase   :int						=			self.scheduler_classes[0]
											lowerCAmelCase   :List[str]						=			self.get_scheduler_config()
											lowerCAmelCase   :List[Any]						=			scheduler_class(**UpperCAmelCase   )

											lowerCAmelCase   :Union[str, Any]						=			[scheduler.config.num_train_timesteps]

											with self.assertRaises(
											    UpperCAmelCase     , msg='`timesteps` must start before `self.config.train_timesteps`: {scheduler.config.num_train_timesteps}}'     , ):
																	scheduler.set_timesteps(timesteps=UpperCAmelCase   )







"""simple docstring"""


from math import sqrt


def        UpperCAmelCase      (					a__ = 1_00_00_00 ):





						'''simple docstring'''






						lowerCAmelCase   :int						=			0
						lowerCAmelCase   :int						=			0
						lowerCAmelCase   :int

						while num_cuboids <= limit:
												max_cuboid_size += 1
												for sum_shortest_sides in range(2     ,      2 * max_cuboid_size + 1 ):
																		if sqrt(sum_shortest_sides**2 + max_cuboid_size**2 ).is_integer():
																								num_cuboids += (
																								    min(a__     ,      sum_shortest_sides // 2 )
																								    - max(1     ,      sum_shortest_sides - max_cuboid_size )
																								    + 1
																								)

						return max_cuboid_size


if __name__ == "__main__":
		print(F"""{solution() = }""")